101,834 research outputs found
Adaptive Selective Sampling for Online Prediction with Experts
We consider online prediction of a binary sequence with expert advice. For
this setting, we devise label-efficient forecasting algorithms, which use a
selective sampling scheme that enables collecting much fewer labels than
standard procedures, while still retaining optimal worst-case regret
guarantees. These algorithms are based on exponentially weighted forecasters,
suitable for settings with and without a perfect expert. For a scenario where
one expert is strictly better than the others in expectation, we show that the
label complexity of the label-efficient forecaster scales roughly as the square
root of the number of rounds. Finally, we present numerical experiments
empirically showing that the normalized regret of the label-efficient
forecaster can asymptotically match known minimax rates for pool-based active
learning, suggesting it can optimally adapt to benign settings
Second-order Quantile Methods for Experts and Combinatorial Games
We aim to design strategies for sequential decision making that adjust to the
difficulty of the learning problem. We study this question both in the setting
of prediction with expert advice, and for more general combinatorial decision
tasks. We are not satisfied with just guaranteeing minimax regret rates, but we
want our algorithms to perform significantly better on easy data. Two popular
ways to formalize such adaptivity are second-order regret bounds and quantile
bounds. The underlying notions of 'easy data', which may be paraphrased as "the
learning problem has small variance" and "multiple decisions are useful", are
synergetic. But even though there are sophisticated algorithms that exploit one
of the two, no existing algorithm is able to adapt to both.
In this paper we outline a new method for obtaining such adaptive algorithms,
based on a potential function that aggregates a range of learning rates (which
are essential tuning parameters). By choosing the right prior we construct
efficient algorithms and show that they reap both benefits by proving the first
bounds that are both second-order and incorporate quantiles
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